A unified compatibility approach to solve certain classical engineering models involving Newtonian fluid flow due to stretching or shrinking surface: A comprehensive study

A unified compatibility method of differential equations is employed to solve some nonlinear two-point boundary value problems arising in the study of the classical model of viscous (Newtonian) fluid flow due to impermeable shrinking and stretching sheets. The solution procedure allows us to find the exact solution of the nonlinear models in the form of a closed-form exponential function. The solution methodology is easy as well as systematic and provides a unified treatment to already known ad hoc solutions of these models found in the literature before. Moreover, some new exact solutions of the various extended versions of this classical engineering boundary layer problem under different physical considerations are discussed. Hence, several misrepresented solutions related to this boundary layer model which are discussed before in the literature are identified, corrected, and clarified in this paper.